Question

Mel plans to save 10,000 dollars per year for 6 years. His first savings contribution is expected in 1 year. He then plans to withdraw 15,200 dollars per year for as long as he can. Mel expects to earn 5.11 percent per year. How many payments of 15,200 dollars can Mel expect to receive if his first annual payment of 15,200 dollars is received in 6 years? Round your answer to 2 decimal places

Answer 1

First, we have to calculate the future value of $10,000 per year for 6 years.
Future value annuity formula = P * [ ((1+r)^n - 1 ) / r ]
Here P = Annuity amount = $10,000
r = interest rate = 5.11% or 0.0511
n = no. of years = 6

Future value at the end of 6 years = $10,000 * [ ((1+0.0511)^6 - 1 ) / 0.0511 ]
= $10,000* 6.820767
= $68,207.67

So the amount in account at the end of 6th year is $68,207.67, Now we will create the withdrawal table.

Here Balance = Beg. balance - Withdrawal
Interest on balance = Balance * 5.11%
Ending Balance = Balance + Interest

Beg. Balance 68,207.67 $ 55,716.36 $ 42,586.75 $ 28,786.21 $ 14,280.47 $ withdrawal 15,200.00 $ 15,200.00 $ 15,200.00 $ 15,200.00 $ 14,280.47 $ Balance Interest on bal. 53,007.67 $ 2,708.69 $ 40,516.36 $ 2,070.39 $ 27,386.75 $ 1,399.46 $ 13,586.21 $ 694.26 $ -0.00 $ -0.00 $ Ending balance 55,716.36 42,586.75 28,786.21 14,280.47 -0.00

Here total payments will be 5, from which 4 payments will be of $15,200 while the last payment will be of $14,280.47 because of insufficient balance in account.